Implicit Differentiation - Basic Idea and Examples

[nurarex]

I NEED HELP PATRICK: dy/dx = dy/dt / dx/dt ... ' if dx/dt not equal to 0' ...I just didn't understand what the heck with that "only if dx/dt is not equal to 0" ?

[SimiSaysRawr]

Thank you so much. This was soooo helpful. <3

[lovelyanimeangel]

You are a math math GOD!! Thanks to you, I was able to understand this, and I'm totally prepared for my Calculus finals tomorrow!

[patrickJMT]

@lovelyanimeangel good luck on the final! : )

[GuitarGirl712]

I SO wish you were my calc teacher! I love your vids, and this one helped me a lot. Hopefully I'll pass my quiz tomorrow...

[Laspher]

Fucking ace.

[nazdeath]

Dude you saved my life. I totally was lost. You cleared doubts! Thanks loads! :)

[clay12349876]

awesome, thanks

[DIGI3COM]

Thanks man, this is helpful and awesome :)

[H0oLIgAnSsRo0lMaRrSz]

love ur handwriting

[kingesteban69]

Sharpies and math... As the other dude said... He's a boss. NOW I can differentiate implicitly lol

[Avitonics]

I feel like crying, not cause im sad or depressed, its because i found your video.. and with your videos i have hope to passing my calculus final

[vqh]

thanks. helped alot

[DragonSniper7]

thank you so much, out of everything in calc 1 i just did not understand how the hell to go about solving these problems

[TaydeeJ]

Thanks so much! You make this so much easier for me to understand than my calc teacher, and he talks for 90 minutes on stuff like this. Lol. Needless to say, I really appreciate your videos.

[Elfmurderer]

Thanks so much, helped me out a lot

[ColumbianKrame]

You explain it so much better than my actual Calc prof!

[11Orly11]

why go to college if i can learn everything on youtube? thanks!

[smstrcklr]

Anyone who does calculus with a sharpie is a boss

[JohnnyCSx]

Thanks man! I'm in AP Calculus in High School, this was taught on Halloween when I was absent and I've been struggling since when this came up. This was a huge help. Thumbs up and subscribe everyone!

[MyShadow15]

Thanks a lot without your help I'd be failing Calculus!

[Dr8co1]

@PatrickJMT have you heard of this formula? dy/dx= -f(x)/f(y)? it's super effective and an extreme shortcut. i don't know what the name is but i LOVE it. i will be posting a video on how to use it and explain it better in words than text lol do you mind if i post it as a vid response?

[wtfudge123]

Permanent marker. Who needs to make mistakes?

[Luckyxseven]

You sir are amazing, I don't understand why professors can't just teach it the way you just did...

[HeartsFable]

Thank you very much. I missed the day of school when he taught this and I have been behind ever since.

[KidKlassic91]

very helpful, especially the intro, I'm towards the end of my calc 1 semster and I'm just now learning why why you use d/dx y dy/dx ... thanks, great stuff

[jfrielx3]

Helping me study for my calc test :)

[kneine15]

wow.... ur 7 min and 6 sec video beats my professor explaining for 2, 3 class. THANKS!!!!

[Alphilles3922]

Pffft, I've got a test tomorrow and I think I love you for this... now, onto the other topics...

[Stooeybear13]

Incredible. Opened up my original notes for my maths course at uni and didnt make any sense to me, your video cured my fear of implicit differentiation. Thanks alot!

[aBalayboa]

amazing...

[juanfhinojosa]

great video!  thanks!

[PreVague]

Yesssss! After days of poring over this...Good lookin out yo'.

[giantmousesdontexist]

thank you sooo much! I have a test on this tomorrow and no one could explain it to me but I get it now. THANKS!

[MarkMe248]

Can I borrow your brain and handwriting for a day? k thanks.

[maltantawi93]

that was amazing!

[rsgirl10]

The d/dx stuff confuses me.

[neenie87]

Calculus is only bearable because of you. Thank you. :)

[shabeer111jan]

good job. thanx for helping us

[theorangeshirts]

I love you Patrick.

[TheYoSkatez]

Why isn't 8 just 0?

[WoZIMoo]

You make me WANT to do cal problems, incredible.

[andyie388]

i love you, thankyou so much, your an inspiration to heros like me everywhere, heaps of help

[WootWootGuitar]

I've watched about 10 of your videos to get ready for my calc midterm tomorrow, and you've said "tedious" in every one

[ronniemonnie]

is

(2x + y)/(8+sin(y)-x) the same thing?

[acdc747e]

Thanks!, This really helped!!

[patrickJMT]

@acdc747e no problem : )

[RyanStarcraftProtoss]

@patrickJMT omg, you are 5x better at explaining this than my teacher. she just tells us how to do it, not why you do it.

[DenemChikn]

can i borrow your brain for like an hour tonight?

[djabz17]

@DenemChikn haha... back of the line

[SuperXD25]

I learn more from you in 7 minutes then from my Math teacher in 7 lessons....

[djabz17]

@SuperXD25 true.

[shortbusrocks46]

Senior in AP Calc... I don't even go to class anymore cause of your videos and I have a 98 in a damn tough class!

[TomK2602]

I've seen the light now...

[hcromett]

I shouldn't even go to class... I learn everything for the test here

[patrickJMT]

@hcromett come watch any time!

[Jezebel1115]

patrickJMT = Math GOD is exactly what you are...Thank you so much for explaining so, that I understand how you're evaluating the problem!

[patrickJMT]

@Jezebel1115 glad i could help : )

[beldonr]

patrickJMT = Math God. Why are there no teachers like you in NY ? The way you explain everything is so clear. Thank you sir !

[kaabii6]

...is it normal to watch your videos and say, out loud, "This all makes sense now!!" Because it has happened to me multiple times. Thank you!

[patrickJMT]

@kaabii6 yes! : )

[limenade155]

ur amazing



[pegleg2060]

Thank you so much for this, i was feeling so lost about what dy/dx even was.

[jld181818]

The angle makes the writing look like the beginning of Star Wars.

[R9378]

Thank you very much for explaining it really clearly. (Unlike my teacher)

I feel like an idiot because I'm usually an ace at math. :S

[Chainsawyourhead]

If you are finding the derivative of 2y, would it be 2(dy/dx) or 2y(dy/dx)

[neenie87]

I have a test in half an hour on this. THANK YOU.

[iantrankinful]

This completely cleared up confusion about dy/dx. My prof wasn't explaining it at all. Thank you so much!

[patrickJMT]

@iantrankinful glad i could help!

[justinartcore]

i'm having trouble with a problem in my homework...it says to "use implicit differentiation of the tangent of the line to the curve at the given point"

2(x^2+y^2)^2=25(x^2-y^2)  given points = (3,1)

[Skytheater]

One question: Isn't the derivative of y, 1? how come you replaced it with (dx/dy)?

[patrickJMT]

@Skytheater cause the derivative of y is not 1, it is 1*dy/dx

[ctnaa]

THANKYOUUUU!!!!!!!!!!

[rowran]

I dont understand how you know which numbers get dy/dx

Thanks your videos have been very helpfull

[GuyNamedCarl]

@rowran If it isn't x, it gets dy/dx.

[caocaobobo1]

Thank you so much, you have cleared so much up.

could you help me with this @_@?

y sqrtx - x sqrt y = 16

I understand you have to do the product rule with u' v + u v' and the dy/dx

but it gets so complicated when i try to work with the -1/2 exponent powers and the sqrts.



[bobbyjoebobbob1]

@caocaobobo1 yeah.. the answer is (2y sqrtx - y sqrt y) / (2x sqrty - x sqrtx) but what are the steps

[shortbusrocks46]

@caocaobobo1 follow the rules and you'll be fine, -1/2 is just another number just as 7 or 6 or 6/2

[envision221]

youre an amazing teacher!!

[EPICT0ASTER]

Can you simplify further and have dy/dx = 1/4 y•csc(y) ?

[MrAvengersAssemble]

It can make things quicker and easier if you just let dy/dx = y'.

[patrickJMT]

@MrAvengersAssemble use whatever notation you prefer.

[Sleepinglarry]

@MrAvengersAssemble Sometimes people just use it because it can sometimes be mistaken for y^1, like @patrickJMT said use whatever you feel comfortable with.

[patrickJMT]

@Sleepinglarry that is exactly correct

[nygiants595]

Awesome! This helps a lot for studying for tests!

[Mushroombob]

I don't always do calculus, but when I do, I use a sharpie on lineless paper

[Ssendecki]

you need to start with College (European High School) Algebra

[patrickJMT]

@Ssendecki i have about 700 high school / college algebra videos on here

[genius10391]

Thank you so much for showing all the steps in this problem. My calculus professor assumes that we can all the algebra in our heads and just shows the first steps and isolating dy/dx. This helped a lot. Thanks again!

[Inurfacegoddamn]

Dude you are awesome, we need more dedicate people like u

[itelluwhat1]

dude you should come and replace my teacher.. because u explained it way better than he did

[khan9980]

you are very good maths teacher respect from PAKISTAN

[MrApendy1]

You are a Math God

[lilweezycashmoney]

this is very clear and easy to understand...but when it comes to my TEST....i blank on everything and i forget how to do them!!! -___-" does that happen to anyone else 0__o

[khan9980]

@lilweezycashmoney yes it happens with my friend.................



[sleepymusicaddict]

@lilweezycashmoney no

[StrawbiBlossoms]

Amazing :D Very helpful! Thank you so much~

[TRlPZ]

I love you.

[msxlillazy]

You've heard this a million times, but I love you. I MIGHT ACTUALLY PASS THIS TEST

[n00beastSH]

and I thought my calc teacher was good! this is great thanks :D

[erinjmui]

THANKS. makes sense now

[wombaston]

I LOVE YOU!!!

[Jules062592]

Dude your a beast. Your so much better than my calc proff and hes a doctor -_-

[craigbchavez12]

umm awesome just saved my life in calc!! thanks a lot

[hilaryiskoolio]

thanks sooooo much!!!!!!!

[parleamimano]

Wow, I'm kind of upset that I paid my school $700 for crappy calc instruction that I doesn't make sense...yet this is making so much sense on youtube. Thanks

[MariscalAle]

you're the best teacher in the world dude thanks so much! i subscribed :)

[diana102393]

THANK YOU! 

[707Cookiez]

THANK YOU SO MUCH!!!

[TheLmhampton]

Thanks. This helped quite a bit. Like others, I'd normally figure it out using the text but my text this semester is bad enough that even my instructor said it stinks. You've cleared up one of the things that's had me virtually pulling my hair out in confusion.

[patrickJMT]

@TheLmhampton tons of calc stuff, come back any time!

[patrickJMT]

@chentity uhhhh

[Almehin]

thanks for that quick explanation. I was able to understand it all because you kept it really simple and you explained every step. keep up the good work.

[patrickJMT]

@Almehin you are very welcome

[CrimsonEdge38]

You and KahnAcademy are saving me this semester. Generally I learn from the same book that my homework is from, but the book this semester is... bad.

Thank you.

[feelikefoxtrot]

I had no idea until i watched this. You are my hero.

[patrickJMT]

@feelikefoxtrot lots of calculus stuff so come back whenever : )

[lei891]

@patrickJMT thanks so much sir!!! you really helped me a lot. ^_^

[SLIMmcGlinn]

You really saved me man. The last math I had was pre-calc, 2 years ago... and now I'm jumping right into calculus. Thanks for the great tutorials!

[blazinpyromaniac]

Can dy/dx be also written as y' ( y prime)? Or is that totally different?

[weststep]

@blazinpyromaniac same thing!

[tiff4annie]

Sorry to bother you but I'm a little unsure about adding dy/dx.

So you add it dy/dx when you want to solve for a derivative that's not x?

[kenie42]

This helped so much, thank you!! and your handwriting is fantastic btw

[elizze6]

What's the difference between d/dx and dy/dx. Because you write the derivative with respect to x as d/dx first but then it turns into dy/dx.

[patrickJMT]

@elizze6 d/dx is the derivative with respect to x (the operation that is being performed) dy/dx is the derivative of a particular function

[Veghead211]

Good description, I was lost on this subject and this has definitely helped.

[Angelgrrl04]

Oh wait, never mind lol

[Angelgrrl04]

3:30 If you use the product rule on (xy), won't you get ((x times y prime) plus (y))

Please let me know asap, thanks.

[orangeZebra03]

OMG your the best teacher in the world. Thank you so much!

[patrickJMT]

@orangeZebra03 thanks very much : ) 

[DemonReacher]

One 10 minute video on youtube > 55 minute lecture at uni. Im seriously considering not even showing up at my stage 1 lectures now, save more time studying other subjects.

[brilliantsam]

Urgh, I'm working through A level papers and I keep forgetting the product rule for 'xy' terms every time I come back to it. >.<

[olyvia33]

u r one great tutor..best tutor i knw..if only i had a lecturer like u..

thx to ur video,i can really understand much better about this implicit differentiation.. (:

[MrKissor]

thank you brother

[deesharkz]

Explained so clearly!

[theajcomp]

Great explanation!

[lmd168]

Why can't university lecturers and tutor explain as clear as you? geez.

Thank you.

[i05h1]

Impressive trick you did there at around 2:00. Best explanation for the mathematically illiterate out there.

[jasperchuwa]

just missed my calculus class today.. thanks to this video, i can catch up no problem! :)

[pauljohn0027]

You're a life saver!!! I wouldn't think of dropping calculus now. :] Thanks!

[blackshatteredhearts]

Thanks so much, you're definitely a life saver. I see hope for my A Levels now!:D

[Agustinoism]

Thank you for this video

[bodybuilder718]

Men and Women everywhere spread the word!!!!!!! i pay good money for a professor that can barely speak English and can not teach worth a damn! my advice, do not listen at all in class, just write the topics and look at these videos! might seem extreme but my A in calculus 2 is proof that this man can make the toughest things look so easy, thanks Patrick you are the man! 8 people that disliked this failed cal just before seeing these videos!

[MrRlabrador]

FREAKING GENIUS! Hope you're getting some good money off those ads!

[dragonkeepar123]

it all makes sense now!

[MrLeatherbreath]

ur awesome man, may many blessing come ur way

[Megabubbajackson]

Holy crap. This is amazing. I might pass Calculus this year D: THANK YOU!

[MisterCloudyDays]

thank you so much

[thebrooksman]

my core 4 exam is this afternoon, why oh why did i only just discover this channel?

[sibityuiop]

I would just like to say a VERY BIG THANK YOU TO YOU! I hope you live for over a 100 years!

[danieljb300]

@sibityuiop if he doesnt, these videos definitely will! Educating young minds even in death..awesome..

[The5854213]

Why didnt I find you before? This was very very helpful..I hope I pass Calc. Again thanks so much for these videos!

[sustantivo1espritu]

im definitely gona share your videos to my classmates who are having problems with this.

[xSabriox]

You are a legend, I'm going to pass mid mid term all thanks to you :D!!

[TARANUS123]

wow cant believe this concept used to give me nightmares, so easy now thanks

[ian559fresno]

Khan Academy isn't bad but I definitely think PatrickJMT makes math much easier and explains things for people who have no clue like me unlike Khan Academy. Thanks for the help, I really appreciate it. Your videos are great and I love how you explain stuff to us like we have no clue so we don't get lost. :)

[DavoC17]

omg dude,

your explanation on this and the chain rule is superb,

you literally explain all the jargon surrounding the notation which is usually my biggest confusion, thanks heaps!

[MrPiPPo]

Give the man the Oscar!

[JKwingfan]

Thank you!



[mtech1020]

you are the idol of my entire calculus class. we worship you

[MiszP2010]

oh you lovely man, thank you so so much! i looked through countless books and internet sites, yet only understood this when i watched your video! fantastic explanation! very clear and concise, not to mention nice handwriting ;)

haha thanks again!

[mrhozer]

What's the term for finding the opposite of this? I'm given dy/dx in a problem and need to find the equation. I'm guessing I need to take the anti-derivative? I'm not sure what the steps are though.

fyi, the problem is dy/dx= x/y^2

[MrHav1k]

Patrick, you have the best Channel on Youtube! THANK YOU SO MUCH! I GET IT NOW!!!

[lambogeek]

This is so helpful, thanks!

[SibirianBlue]

thankyouthankyouthankyouthanky­outhankyou! :)

[nibh37]

you are a genius!!!

i had no clue what my math professor was talking about

but after watching your video, i think i do!!

[2cutensweet2h8]

I absolutely love you. Thank you!!! More reason to not go to my Calc and Trig lectures!! - Joke.

[spliff42007]

you have opened my world mathematically

[JohnRater]

hey man if I revolutionize the computer industry and make billions in the process I'll make sure to cut you a check for a million bux or something

[jackxzx]

patrick! i'll pray for you every single day!

you are simply the best! i still thank God for letting me click at your video!

[youarepwned]

So why is it that when you derive from cos(y) you go to -sin(dy/dx), but when deriving the 8y, you write 8dy/dx? I am not asking about why you went from cos to -sin, I understand that; I just don't know why we keep the y on the cosy step, but you substituted the y on the 8y part.

I'd ask my teacher, but she's very condescending and generally tells us to go figure it out on our own.

[sgtdoyle28]

in 10 mins of your vids, ive learned more than 2 months with my teacher

[AlwaysBeMyThunder21]

What is the actual definition of differentiation?

thx for the vid btw! :)

[20thCenturyG4M1NG]

Hey baby, I wish I could be your derivative so I could lay tangent to your curves. ;)

[MrXamenyap]

my worst topic .....=( as well as intergation

[jak68k]

best calc teaching period.

[patrickJMT]

@jak68k thanks!

[dajakesta1234]

@patrickJMT dude how old r u??

[FabButterfly]

i love you. you're saving my life right now!

[iknowsnothin]

math with you is filled with "thats what she said" jokes. Oh the sexiness.